Chapter 1.4, Problem 35E

Let $L_1$ and $L_2$ be two nonvertical straight lines in the plane with equations $y=m_{1}x+b_1$ and $y=m_{2}x+b_2$, respectively. Find conditions on $m_1$, $m_2$, $b_1$, and $b_2$ such that (a) $L_1$ and $L_2$ do not intersect, (b) $L_1$ and $L_2$ intersect at one only one point, and (c) $L_1$ and $L_2$ intersect infinitely many points.